Subgroups — #3663⋊C₃ #88474

Order 432.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic
2	C₈×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
3	3₋¹⁺²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×ΓL(1,𝔽₂₅)	—	3	1	no	maximal
5	#3663	C₃	1	1	yes	maximal, characteristic, complemented
6	C₂×AGL(1,ℤ/9)	C₄	1	1	yes	characteristic
7	C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
8	3₋¹⁺²⋊C₄	C₄	1	1	yes	characteristic
9	C₃×C₄×D₃	—	3	1	no	—
10	C₃²×C₈	D₃	1	1	yes	characteristic
11	C₃×C₃⋊C₈	—	3	1	no	—
12	C₄×D₉	C₂×C₃	1	1	yes	characteristic
13	C₈×C₉	—	2	1	no	—
14	C₈×C₉	C₂×C₃	1	1	yes	characteristic, complemented
15	C₉⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
16	C₂×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
17	AGL(1,ℤ/9)	—	2	1	no	—
18	C₃×M₁₆	—	9	1	no	—
19	ΓL(1,𝔽₂₅)	—	3	1	no	—
20	C₂×C₃×D₃	—	3	1	no	—
21	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
22	C₃×Dic₃	—	3	1	no	—
23	C₂×D₉	C₃×C₄	1	1	yes	characteristic
24	C₄×C₉	—	2	1	no	—
25	C₄×C₉	C₂²×C₃	1	1	yes	characteristic
26	Dic₉	C₃×C₄	1	1	yes	characteristic
27	3₋¹⁺²	M₁₆	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃×C₄	—	9	1	no	—
29	C₄×D₃	—	3	1	no	—
30	C₃×C₈	—	3	1	no	—
31	C₃×C₈	—	9	1	no	—
32	C₃×C₈	C₃×D₃	1	1	yes	characteristic
33	C₃⋊C₈	—	3	1	no	—
34	C₂×C₃²	C₄×D₃	1	1	yes	characteristic
35	C₃×D₃	—	6	1	no	—
36	C₂×C₉	—	2	1	no	—
37	C₂×C₉	C₂×C₃×C₄	1	1	yes	characteristic
38	D₉	—	2	1	no	—
39	M₁₆	—	9	1	no	Sylow
40	C₂²×C₃	—	9	1	no	—
41	C₂×D₃	—	3	1	no	—
42	C₃×C₄	—	3	1	no	—
43	C₃×C₄	—	9	1	no	—
44	C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
45	Dic₃	—	3	1	no	—
46	C₃²	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
47	C₉	—	2	1	no	—
48	C₉	C₃×M₁₆	1	1	yes	characteristic, complemented
49	C₂×C₄	—	9	1	no	—
50	C₈	—	9	1	no	—
51	C₈	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
52	C₂×C₃	—	3	1	no	—
53	C₂×C₃	—	18	1	no	—
54	C₂×C₃	C₃×C₄×D₃	1	1	yes	characteristic
55	D₃	—	6	1	no	—
56	C₂²	—	9	1	no	—
57	C₄	—	9	1	no	—
58	C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
59	C₃	—	3	1	no	—
60	C₃	C₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
61	C₂	—	18	1	no	—
62	C₂	C₄×AGL(1,ℤ/9)	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×AGL(1,ℤ/9)
commutator	C₂×C₉	C₂×C₃×C₄
Frattini	C₃×C₄	C₂×C₃×D₃
Fitting	C₈×3₋¹⁺²	C₂
socle	C₂×C₃	C₃×C₄×D₃
prime radical	C₂×AGL(1,ℤ/9)	C₄
cosocle	C₄×C₉	C₂²×C₃
hypercenter	C₈	AGL(1,ℤ/9)
hypocenter	C₉	C₃×M₁₆
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄ ◁ C₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₈×3₋¹⁺²	C₂	semidirect
3. 3₋¹⁺²⋊C₈	C₂	semidirect
5. #3663	C₃	semidirect
14. C₈×C₉	C₂×C₃	semidirect
15. C₉⋊C₈	C₂×C₃	semidirect
27. 3₋¹⁺²	M₁₆	semidirect
48. C₉	C₃×M₁₆	semidirect
51. C₈	AGL(1,ℤ/9)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×AGL(1,ℤ/9)	2
C₈×3₋¹⁺²	2
3₋¹⁺²⋊C₈	2
C₃×ΓL(1,𝔽₂₅)	3
#3663	3

Subgroups — #3663⋊C3 #88474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3663⋊C₃ #88474